The present invention relates to sensors and related methods and computer program products, and more particularly, to mass flow measurement methods, apparatus, computer program products.
Many sensor applications involve the detection of mechanical vibration or other motion. Examples of sensors that utilize such motion detection include Coriolis mass flowmeters and vibrating tube densitometers. These devices typically include a conduit or other vessel that is periodically driven, i.e., vibrated. Properties such as mass flow, density and the like associated with a material contained in the conduit or vessel may be determined by processing signals from motion transducers positioned on the containment structure, as the vibrational modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit or vessel structure and the material contained therein.
A typical Coriolis mass flowmeter includes one or more conduits that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibrational modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, a conduit is excited at resonance in one of its natural vibrational modes as a material flows through the conduit, and motion of the conduit is measured at points along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Exemplary Coriolis mass flowmeters are described in U.S. Pat. Nos. 4,109,524 to Smith, 4,491,025 to Smith et al., and Re. 31,450 to Smith.
Unfortunately, the accuracy of conventional Coriolis mass flowmeters may be compromised by nonlinearities and asymmetries in the conduit structure, motion arising from extraneous forces, such as forces generated by pumps and compressors that are attached to the flowmeter, and motion arising from pressure forces exerted by the material flowing through the flowmeter conduit. The effects of these forces are commonly reduced for by using flowmeter designs that are balanced to reduce effects attributable to external vibration, and by using frequency domain filters, e.g., bandpass filters designed to filter out components of the motion signals away from the excitation frequency. However, mechanical filtering approaches are often limited by mechanical considerations, e.g., material limitations, mounting constraints, weight limitations, size limitations and the like, and frequency domain filtering may be ineffective at removing unwanted vibrational contributions near the excitation frequency.
According to embodiments of the invention, mass flow of a material in a conduit is estimated by mode selective filtering a plurality of motion signals representing motion of the conduit to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the conduit. A plurality of phase estimates is generated from the plurality of mode selective filtered motion signals. A mass flow estimate is generated from the plurality of phase estimates. The plurality of phase estimates may be estimated using a phase reference derived from one of the plurality of mode selective filtered motion signals.
In some embodiments of the invention, a modal transformation is applied to the plurality of motion signals to generate a plurality of modal response signals in a modal coordinate domain. A mode selective transformation is applied to the plurality of modal response signals to generate the plurality of mode selective filtered motion signals. In other embodiments of the invention, a frequency of a mode selective filtered motion signal of the plurality of mode selective filtered motion signals is estimated. Quadrature first and second reference signals are generated based on the estimated frequency. The plurality of phase estimates is generated from the plurality of mode selective filtered motion signals and the first and second reference signals.
In still other embodiments of the invention, a plurality of time difference estimates is generated from the plurality of phase estimates, and the mass flow estimate is generated from the plurality of time difference estimates. The plurality of time difference estimates may be generated from the plurality of phase estimates by dividing the plurality of phase estimates by a mode frequency to generate a plurality of time difference values. A plurality of zero-flow reference time differences may be applied to the plurality of time difference values to generate the plurality of time difference estimates. The mode frequency may be estimated from a modal motion signal generated from the plurality of motion signals. Density of material in the conduit may also be estimated from the estimated mode frequency.
According to other aspects of the invention, mass flow of a material in a conduit may be determined by processing a plurality of motion signals representing motion of the conduit using one of the plurality of motion signals as a timing reference to generate a like plurality of difference estimates, and estimating a slope parameter of a scaling function that relates the plurality of difference estimates to a like plurality of reference differences representing motion of the conduit at a known mass flow. A mass flow estimate may be estimated from the estimated slope parameter and the known mass flow.
In some embodiments of the invention, an augmented matrix including the plurality of reference differences is generated. The plurality of difference estimates is multiplied by a pseudoinverse of the augmented matrix to determine the slope parameter. In other embodiments, the plurality of difference estimates is multiplied by a pseudoinverse of the reference time differences to determine the slope parameter. The scaling parameter can also be iteratively estimated to determine the slope parameter, using, for example, a Least Mean Square (LMS) estimation procedure.
According to other aspects of the invention, an apparatus includes a conduit configured to contain a material. A plurality of motion transducers is operatively associated with the conduit and operative to produce a plurality of motion signals representing motion of the conduit. A signal processing circuit receives the plurality of motion signals and mode selective filters the plurality of motion signals to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the conduit. The signal processing circuit generates a plurality of phase estimates from the plurality of mode selective filtered motion signals, and generates a mass flow estimate from the plurality of phase estimates. The signal processing circuit may generate the plurality of phase estimates using a phase reference derived from one of the plurality of mode selective filtered motion signals.
According to still other embodiments of the invention, an apparatus includes a conduit and a plurality of motion transducers, operatively associated with the conduit, that generate a plurality of motion signals representing motion of the conduit. A signal processing circuit receives the plurality of motion signals and processes the plurality of motion signals using one of the plurality of motion signals as a timing reference to generate a like plurality of difference estimates. The signal processing circuit estimates a slope parameter of a scaling function that relates the plurality of difference estimates to a like plurality of reference differences representing motion of the conduit at a known mass flow, and generates a mass flow estimate from the estimated slope parameter and the known mass flow. The signal processing circuit may generate an augmented matrix including the plurality of reference differences, and may multiply the plurality of difference estimates by a pseudoinverse of the augmented matrix to determine the slope parameter. Alternatively, the signal processing circuit may multiply the plurality of difference estimates by a pseudoinverse of the reference time differences to determine the slope parameter. The signal processing may also iteratively estimate the scaling function.
According to other aspects of the invention, a computer program product for estimating mass flow of a material in a conduit includes a computer-readable storage medium having computer-readable program code embodied in the computer-readable storage medium. The computer-readable program code includes mass flow estimating computer-readable program code that mode selective filters a plurality of motion signals representing motion of the conduit to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the conduit, that generates a plurality of phase estimates from the plurality of mode selective filtered motion signals, and that generates a mass flow estimate from the plurality of phase estimates. The mass-flow estimating computer-readable program code may generate the plurality of phase estimates using a phase reference derived from one of the plurality of mode selective filtered motion signals. For example, the mass flow estimating computer-readable program code may estimate a frequency of a mode selective filtered motion signal of the plurality of mode selective filtered motion signals, generate quadrature first and second reference signals based on the estimated frequency, and generate the plurality of phase estimates from the plurality of mode selective filtered motion signals and the first and second reference signals.
According to other embodiments, the mass flow estimating computer-readable program code generates a plurality of time difference estimates from the plurality of phase estimates and generates the mass flow estimate from the plurality of time difference estimates. The mass flow estimating computer-readable program code may apply a modal transformation to the plurality of motion signals to generate a modal motion signal in a modal coordinate domain, estimate a mode frequency from the modal motion signal, and generate the plurality of time difference estimates from the plurality of phase estimates using the estimated mode frequency. The computer-readable program code may further include density estimating computer program code that estimates density of material in the conduit from the estimated mode frequency.
According to yet other aspects of the invention, computer-readable program code embodied in a computer-readable storage medium includes mass flow estimating computer-readable program code that processes a plurality of motion signals representing motion of the conduit using one of the plurality of motion signals as a timing reference to generate a like plurality of difference estimates, that estimates a slope parameter of a scaling function that relates the plurality of difference estimates to a like plurality of reference differences representing motion of the conduit at a known mass flow, and that generates a mass flow estimate from the estimated slope parameter and the known mass flow. The mass flow estimating computer-readable program code may generate an augmented matrix including the plurality of reference differences and multiply the plurality of difference estimates by a pseudoinverse of the augmented matrix to determine the slope parameter. Alternatively, the mass flow estimating computer-readable program code may multiply the plurality of difference estimates by a pseudoinverse of the reference time differences to determine the slope parameter. The mass flow estimating computer-readable program code may also iteratively estimate the scaling function.